find dy for the given values of x and δx. y=x³ - 5x² + 8; x = 1; δx = - 0.5 dy = (type an integer or a…
find dy for the given values of x and δx. y=x³ - 5x² + 8; x = 1; δx = - 0.5 dy = (type an integer or a decimal.)
Answer
Explanation:
Step1: Find the derivative of y
The derivative of $y = x^{3}-5x^{2}+8$ using the power - rule $\frac{d}{dx}(x^{n})=nx^{n - 1}$ is $y^\prime=\frac{dy}{dx}=3x^{2}-10x$.
Step2: Evaluate the derivative at x = 1
Substitute $x = 1$ into $y^\prime$: $y^\prime(1)=3(1)^{2}-10(1)=3 - 10=-7$.
Step3: Use the differential formula
The differential formula is $dy=y^\prime(x)\Delta x$. We know $y^\prime(1)=-7$ and $\Delta x=-0.5$. Then $dy=(-7)\times(-0.5)$.
Answer:
3.5